Equivalent Frequency Research Articles

Equivalent circuit of an inductor on a nanocrystalline core with a high magnetic permeability

Based on the measured impedance of the inductors based on a toroidal core wound from a thin (18 m) nanocrystalline tape, with a different number of winding turns, an equivalent high frequency (0 Hz - 500 MHz) circuit model was built. The equivalent circuit model was built taking into account the physical processes occurring in the inductor: effect of wire resistance, effect of core material, mutual effect of wire and core material. The attempt explaining why the frequency characteristics (modulus and phase) of the inductor complex impedance have such a character in a wide frequency band (up to 500 MHz) was made. It was shown that for constructing an equivalent circuit model (structure and parameters), measuring only the inductors resistance modulus is not enough. It is also necessary to measure the phase of the inductor complex resistance, which is ignored in many works on the synthesis of an e inductor equivalent circuit. The fundamental difference between the operation of a nanocrystalline core and a ferrite core as applied to high-frequency filters is shown.

Improved equation to describe the induction motor currents during nearby three‐phase short‐circuits

AbstractThis article shows an improved equation to describe the induction motor currents during a three‐phase short‐circuit near to motor terminals. The proposed equation considers three details which are not in the equation shown in the IEEE Std. 551: (a) the equivalent frequency of these currents is not strictly equal to the grid frequency; (b) the magnitude of the DC component is not strictly equal to the magnitude of the AC component; (c) an angle is included to consider the instant of fault occurrence. The proposed equation was verified by experimental results, which were also verified by simulations. It is shown that the equivalent frequency of analysed currents is not exactly the grid frequency due to the sudden change of the machine speed (caused by the high braking torque originated by high transient currents during the short‐circuit). This effect is larger in smaller motors. The AC and DC components of the analysed currents have their own time constants, which are usually estimated from motor equivalent circuit. The application of the improved equation was useful to demonstrate that such a procedure does not lead to accurate results in case of the DC time constants of small motors. Finally, an example illustrates a case that cannot be well described by the equation from the IEEE Std. 551, whereas the result from the proposed equation is very similar to the measured current.

An Improved Synthesis Phase Unwrapping Method Based on Three-Frequency Heterodyne

An improved three-frequency heterodyne synthesis phase unwrapping method is proposed to improve the measurement accuracy through phase difference and phase sum operations. This method can reduce the effect of noise and increase the equivalent phase frequency. According to the distribution found in the phase difference calculation process, the Otsu segmentation is introduced to judge the phase threshold. The equivalent frequency obtained from the phase sum is more than those of all projected fringe patterns. In addition, the appropriate period combinations are also studied. The simulations and related experiments demonstrate the feasibility of the proposed method and the ability to improve the accuracy of the measurement results further.

Seismic response of a nuclear island building with base isolation considering the soil–structure interaction effect

AbstractThis study aims to investigate the influence of soil–structure interaction (SSI) on the seismic response of a nuclear island (NI) building with base isolation. Hence, modal and dynamic time‐history analyses of the NI building with base isolation based on different soil dynamic numerical models that are applicable for homogeneous and layered sites to consider the SSI effect were conducted. After a comparison analysis of natural frequencies, floor response spectra (FRS), and acceleration response of superstructure, the following results are obtained. (i) For homogeneous sites, the degrees of freedom of the horizontal translation and torsion of the NI building with base isolation calculated using different site dynamic numerical models have equivalent natural frequencies. For layered sites, the natural frequencies increase slightly with the improvement of the shear wave velocity of the upper layered soil. (ii) For homogeneous sites, FRS calculated by the massless foundation model is generally larger than those of the dynamic model proposed by the ASCE code and the viscoelastic artificial boundary site model. Both the spectral and peak values of horizontal FRS at a low frequency band calculated by considering the SSI effect are larger than those without the SSI effect. (iii) For layered sites, both the spectral and peak values of horizontal FRS at a low frequency band have an amplification effect compared with that of a homogeneous site. (iv) For layered sites, the calculated horizontal acceleration response does not have evident law that changes with the degree of hardness and softness of the upper soil. Therefore, the SSI effect for particular homogeneous and layered sites should be considered when calculating the seismic response of the NI building with base isolation.

High Bandwidth Series-Form Switch-Linear Hybrid Envelope Tracking Power Supply With Reduced Bandwidth Envelope and Step-Wave Edge Adjustment Methods

The series-form switch-linear hybrid envelope tracking (ET) power supply is constituted by a multilevel converter and a linear amplifier connected in series, featuring high efficiency and wide tracking bandwidth. With the development of wireless communication, the envelope bandwidth of the radio-frequency signal reaches tens of megahertz and even hundreds of megahertz, leading to a high switching loss in the multilevel converter and thus degraded overall efficiency of the ET power supply. To reduce the switching loss and ensure high tracking bandwidth, this article proposes to let the multilevel converter track the reduced bandwidth envelope signal and the linear amplifier track the original one. Then, a step-wave edge adjustment method is proposed to adjust or eliminate the rising and falling edges of the step-wave voltage for further reducing the equivalent switching frequency of the multilevel converter and the voltage across the power device of the linear amplifier. As a result, the switching loss in the multilevel converter and the power loss in the linear amplifier could be reduced, leading to a notably higher overall efficiency. A prototype with 40 MHz tracking bandwidth, 7–27 V output voltage, and 15 W average output power is fabricated and tested in the lab, and the experimental results are provided to verify the effectiveness of the proposed method.

A Phase-Disposition PWM-Enabled Model Predictive Control for a Nine-Level Inner-Interleaved Hybrid Multilevel Converter

This article brings forward a phase-disposition pulsewidth modulation-enabled model predictive control (PDPWM-MPC) for a nine-level inner-interleaved hybrid multilevel converter (9L-IHMC). First, three layers of virtual space vector diagrams (VSVDs) are established based on the sign patterns of the original and virtual reference vectors in the abc-frame to achieve the phase-disposition pulsewidth modulation (PD-PWM) in a nonindependent three-phase way. Then, three adjacent virtual vectors in the third-layer VSVD, together with their optimized duty cycles, are applied to guarantee the optimal current tracking. Finally, through the use of the duty-cycle alternation approach, dc-link and floating capacitors voltages are balanced and circulating currents are mitigated as well. The proposed PDPWM-MPC can not only enable the decoupling of the low- and high-frequency stages in the 9L-IHMC but also reduce both output current ripples and computational burden. In addition, it can achieve a constant equivalent switching frequency and address the disproportion of power losses associated with the PD-PWM. Both simulations and experiments on a silicon carbide device-based prototype substantiate the effectiveness of the proposed control strategy.

EMI-Regulated SiC-Based Motor Drives With Markov Chain Pseudo-Random Frequency Space Vector Pulse Width Modulation Strategy

Compared with traditional silicon-based (Si) power devices, wide-bandgap (WBG) power devices have broader application prospects in AC motor drive due to their high-temperature reliability, low conduction, and switching losses. However, a fast switching process and high switching frequency will cause more serious conducted electromagnetic interference (EMI) emission. To solve the problem, this paper proposed a pseudo-random frequency space vector pulse width modulation (PRF-SVPWM) strategy based on a carrier with a pseudo-random frequency. There are two sawtooth waves with the same frequency but opposite phases as alternatives. The proposed method randomly selects only one sawtooth wave during a complete control period. After random combination, the generated carrier is no longer a regular sawtooth wave. This new carrier contains 4 different modes including 2 sawtooth (positive and negative) and 2 triangular waves (positive and negative). A 2-state Markov chain is introduced to produce a PRF control signal which is regarded as the law of choice. In this way, the equivalent switching frequency keeps constant but the real-time switching frequency will randomly vary within the determined range. EMI emission level can be significantly reduced. The effectiveness of the proposed PRF-SVPWM is verified by several sets of experiment results.

Investigation of Frequency Models to Predict Dynamic Behavior of ESD Protection Networks

With the shrinking dimension of technologies and safety requirements, electrostatic discharge (ESD) protections play a more and more important role. Consequently, the prediction of the transient behavior's protection network is becoming difficult for system level designers in order to guarantee systems safety. A model reproducing the turn- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> behavior is needed to obtain a precise simulation's protection strategy network, especially during the protection triggering. In this article, we propose a complete measurement and computation setup to access an equivalent frequency model of devices under strong pulse injections for a rapid model construction. Details of the measurement and data computation to obtain a frequency model using a transmission line pulse generator combined with time-domain reflectometry measurement will be provided. To validate our proposed frequency model, a comparison between the measurements and simulations is first performed on passive and linear components, and then on two protection devices (transient voltage suppressor). A simulation on a protection network, at the board level, will show that the combination of the frequency models could be done to predict its response to ESD pulse with an acceptable precision, without the tedious step of component modeling.

Vortex-induced vibration of a circular cylinder with nonlinear restoring forces at low-Reynolds number

The numerical simulation of two-dimensional flows around an elastically-mounted circular cylinder on a linear/quadratic spring configuration at low-Reynolds number (Re) is conducted in order to study the vortex-induced vibration (VIV) of the system. The extent of Re used in this study range from 50 to 150 inclusive. The data obtained from the numerical simulations are used to investigate the impact of the nonlinearity in the spring configuration on the VIV response of the dynamical system. The equivalent natural frequency for a circular cylinder supported elastically on a linear/quadratic spring is derived and found to depend on the square root of the maximum amplitude of the transverse displacement. The range of Re associated with the initial branch of the response is increased (extended) and the upper and lower branches are suppressed (almost disappearing when the hardening nonlinearity is sufficiently strong) for an elastically-mounted cylinder on a linear/quadratic spring configuration compared to that for the same cylinder supported elastically on a linear spring. The detailed characteristics (e.g., vortex shedding modes, amplitude and oscillation frequency of the transverse displacement, etc.) of the lock-in range and the transition out of this range for the VIV system as a function of increasing Re is studied using power spectrum, phase portrait and dynamical mode decomposition analysis. The information obtained from the analysis is synthesized in order to investigate the different physical mechanisms and phenomena appearing in the VIV system and how these are linked to the underlying vortex shedding and amplitude response regimes (initial branch, upper branch, desynchronization branch) of the dynamics of the fixed (stationary) and elastically-mounted cylinder.

Analysis of Induced Current on Power Transmission Lines for the Reradiation Interference in Medium Wave Based on Characteristic Modes

The reradiation interference from power transmission lines (PTL) on the adjacent wireless stations is directly caused by the induced current on metal parts, which means the interference could be suppressed by reducing the induced current. In order to effectively analyze the induced current of PTL, a method for analyzing induced current on PTL based on characteristic modes is proposed combining MoM with intrinsic modes. This method breaks through the traditional antenna resonance theory proposed by IEEE and could effectively avoid model equivalent defects and frequency limitations of traditional methods. Firstly, a generalized characteristic equation about the characteristic mode currents of PTL is constructed, and the numerical solutions of the characteristic mode currents are obtained by the idea of a discrete solution. Then, through the weighted orthogonal relationship between different characteristic mode currents, the expansion coefficients of the characteristic mode currents are obtained; finally, combined with the Poynting theorem, the physical meaning of the expansion coefficients and their related quantities are explained from the perspective of energy and the analysis of the induced current is realized from the physical level. The results of the example analysis show that the error between the peak frequencies of the induced current calculated by the method in this paper and the peak frequencies calculated by MoM does not exceed 2.46% and the method in this paper can well explain the disappearance of the “double wavelength loop resonance frequency” under the excitation of a vertically polarized plane wave.

A Step-Down Resonant Modular Multilevel DC/DC Converter With Extendable ZVS Range Based on Asymmetric Triangular Current

In this article, a new step-down resonant modular multilevel dc/dc converter is proposed for medium-voltage applications. The proposed converter is derived from the combination of the modular multilevel converter (MMC) and resonant converter with a passive auxiliary circuit. It can achieve zero voltage switching (ZVS) over a wide input voltage range for all switches compared with the conventional dc/dc MMC. Specifically, the asymmetric triangular compensating current provided by the passive auxiliary circuit is first introduced to flow into the bridge arms. Then, the current bias caused by the MMC structure is eliminated in the lower side switches of the submodules to achieve ZVS. Moreover, asymmetrical pulsewidth modulation is applied to double the equivalent switching frequency and obtain a high step-down ratio. In this way, the resonant current is reduced, and the conversion efficiency is improved. Besides, the simulation and experimental results of the prototype are presented to demonstrate the viability of the proposed converter. The results convincingly verify the ability of the proposed converter to offer ZVS for all the switches over a wide input voltagerange.

Phase Noise Analysis of Separately Driven Ring Oscillators

In this paper, for the first time, the phase noise analysis of a Multi-loop Skew based Single Ended Oscillator (MSSROs) is derived and validated. Compared to the three stages of conventional ring oscillators (CROs), SDROs provide an equivalent oscillation frequency with improved phase noise with increasing stages. The primary distinction between these two designs (SDRO and three-stage CROs) is the inherent skew offset between the PMOS/NMOS gates caused by the unique connection. This skew offset is the fundamental cause of delay cell noise suppression; the SDROs have loosely coupled oscillators that run concurrently, forming multiple 3-stages of separately driven Ring Oscillators. As a result, a shaping function is derived in terms of skew offset, and simulating these with varying skew offset results in suppressing behavior. Additionally, we derived phase noise for a skew-based design and validated it in PDKs of 180nm and 65 nm. We plotted the thermal (flicker) noise contribution and found that increasing the number of stages leads to an approximately 1-2 dB reduction in phase noise while maintaining the same NMOS/PMOS size ratio. Finally, a 2-3 dB reduction in phase noise is achieved in MSSROs by incorporating the shaping function into phase noise equations.

Complete Stability Analysis and Optimization of the Extended Delayed Resonator With Virtual Natural Frequency Adjustment

AbstractThe delayed resonator (DR) is known for its ideal vibration suppression and simple control logic, but its operable frequency range is also known limited due to stability issues and practical hardware constraints. To extend the limited operable frequency range, we inject an additional nondelayed control term into the feedback loop of the classic DR such that the equivalent natural frequency of the DR can be real-time tuned, so the creation of DR with virtual natural frequency adjustment (DRV). Besides, we take the difference between the adjustable natural frequency of the DRV and the excitation frequency as a control parameter to further enhance the vibration suppression leading to optionally tuned parameters for a given excitation. For this, we start with the complete stability analyses of the DRV and the associated coupled system following independent and purely analytical approaches, and the obtained nonconservative stability maps reveal DRV's greatly extended operable frequency range. Given the optional tuned parameters, an optimization procedure aiming for a faster transient process and stronger robustness is proposed to determine the optimal parameter composition. Finally, three numerical case studies are prepared to demonstrate the benefits of the DRV compared with the classic DR. In addition to extending the operable frequency range of the classic DR, this work simplifies the stability analysis of the existing DR investigations and provides a guideline for the tuned control parameter design if they are optional.

Stepwise development of atmospheric pressure plasma jet driven by bursts of high-voltage nanosecond pulses at multi-tens MHz

This study employs the bursts of high-voltage nanosecond pulses at multi-tens MHz to drive the helium atmospheric pressure plasma jet. Such bursts are obtained by modulating a high-voltage nanosecond pulse based on the wave reflections in a coaxial cable. The development processes and mechanisms of the plasma jet are analyzed in detail based on the discharge waveforms, discharge images, gas temperature, electron density, and axial electric field. Because the time interval between adjacent pulses is much shorter than the characteristic plasma decay time, the discharge channel driven by the first pulse still has high residual electron density and conductivity when the second pulse arrives. The first discharge channel serves as an extension of the high-voltage electrode. In this case, the second discharge starts at the end of the first discharge channel and continues to propagate forward. Driven by the bursts of high-voltage nanosecond pulses, the stepwise propagation of a guided streamer along the plasma jet is observed. The characteristic of the stepwise development of the guided streamer is stable and repeatable under the same condition and does not change at different helium flow rates if the flow is laminar. Reducing the cable length results in a higher equivalent pulse frequency in the bursts and significantly increases the plasma jet length. However, an excessively high frequency will cause a rise in gas temperature and pressure fluctuation in helium flow, resulting in a reduction in the length of the laminar region and an unstable discharge.

A Hybrid Multivector Model Predictive Control for an Inner-Interleaved Hybrid Multilevel Converter

A hybrid multivector model predictive control strategy for an inner-interleaved hybrid multilevel converter is brought forward in this article, which can enable the separation of the low- and high-frequency stages. It initiates with the use of sign patterns of the reference vector in the stationary reference frame to determine switching states of the low-frequency stage. Then, the reference vector is converted to the inner virtual space vector diagram, which is further transformed into a 120° oblique coordinate system, where the adjacent vectors are selected. Further, the current tracking is realized through the duty cycle optimization of the chosen vectors. Finally, a symmetric switching sequence (SS), which serves as the best one for dc capacitors voltages balancing and circulating current suppression, is selected among all the SSs that belong to the three chosen vectors with optimal duty cycles. The proposed method reduces both current ripples and computational burden while achieving a constant equivalent switching frequency. Comprehensive experimental results performed on an all silicon-carbide prototype verify the effectiveness of the proposed control.

Performance Warning of Bridges under Train Actions through Equivalent Frequency Response Functions

Performance Warning of Bridges under Train Actions through Equivalent Frequency Response Functions

Equivalent circuit of a dielectric in a wide frequency range (0 Hz – 500 MHz)

Based on the measured impedance of the dielectrics an equivalent high frequency (0 Hz - 500 MHz) circuit model was built. The equivalent circuit model was built taking into account the physical processes occurring in the dielectric. The attempt explaining why the frequency characteristics (modulus and phase) of the dielectric complex impedance have such a character in a wide frequency band (up to 500 MHz) was made. It was shown that for constructing an equivalent circuit model (structure and parameters), measuring only the dielectrics resistance modulus is not enough. It is also necessary to measure the phase of the dielectric complex resistance, which is ignored in many works on the synthesis of an e dielectric equivalent circuit.

Complex permittivity measurement technique using metamaterial broadside coupled split ring resonator

A simple and effective method for the determination of complex permittivity of dielectric materials at microwave frequencies using a Broadside Coupled Split Ring Resonator (BCSRR) metamaterial structure is presented. A single BCSRR unit cell placed between the transmitting and receiving probes of a Vector Network Analyzer (VNA) is used as the test probe. Resonance frequencies and bandwidths of transmission curves, measured with and without the sample placed over the BCSRR test probe, are used to determine the real and imaginary parts of the complex permittivity by treating the BCSRR as an LC resonant circuit. Relevant equations connecting equivalent capacitance and resonance frequencies are derived from the basic equivalent circuit parameters of the BCSRR through a quasi-static analysis by considering the fringing fields in its vicinity, especially on the top and bottom. Accuracy of the theoretical formula derived for determining the complex permittivity using the BCSRR is verified through experiments and simulations.

Auditory clicks elicit equivalent temporal frequency perception to tactile pulses: A cross-modal psychophysical study.

Both hearing and touch are sensitive to the frequency of mechanical oscillations—sound waves and tactile vibrations, respectively. The mounting evidence of parallels in temporal frequency processing between the two sensory systems led us to directly address the question of perceptual frequency equivalence between touch and hearing using stimuli of simple and more complex temporal features. In a cross-modal psychophysical paradigm, subjects compared the perceived frequency of pulsatile mechanical vibrations to that elicited by pulsatile acoustic (click) trains, and vice versa. Non-invasive pulsatile stimulation designed to excite a fixed population of afferents was used to induce desired temporal spike trains at frequencies spanning flutter up to vibratory hum (>50 Hz). The cross-modal perceived frequency for regular test pulse trains of either modality was a close match to the presented stimulus physical frequency up to 100 Hz. We then tested whether the recently discovered “burst gap” temporal code for frequency, that is shared by the two senses, renders an equivalent cross-modal frequency perception. When subjects compared trains comprising pairs of pulses (bursts) in one modality against regular trains in the other, the cross-sensory equivalent perceptual frequency best corresponded to the silent interval between the successive bursts in both auditory and tactile test stimuli. These findings suggest that identical acoustic and vibrotactile pulse trains, regardless of pattern, elicit equivalent frequencies, and imply analogous temporal frequency computation strategies in both modalities. This perceptual correspondence raises the possibility of employing a cross-modal comparison as a robust standard to overcome the prevailing methodological limitations in psychophysical investigations and strongly encourages cross-modal approaches for transmitting sensory information such as translating pitch into a similar pattern of vibration on the skin.

A Hybrid Model Predictive Control With Integrated Phase-Disposition and Phase-Shifted PWM for an Inner-Interleaved Hybrid Multilevel Converter

This article puts forward a hybrid model predictive control (H-MPC) for an inner-interleaved hybrid multilevel converter (IHMC). The sign patterns of the original and shifted reference vectors in the original and virtual space vector diagrams (VSVDs) are used, respectively, to realize the phase-disposition pulsewidth modulation (PWM) and determine the low-frequency switching states. Then, the three adjacent vectors are selected in the second-layer VSVD and the optimal current tracking is safeguarded by the duty cycle optimization of the three adjacent vectors. Finally, through applying the phase-shifted PWM to the two interleaved legs, a constant and doubled equivalent switching frequency can be achieved, which further paves the way for dc-link and floating capacitor voltages balancing and circulating current mitigation with the use of the straightforward duty cycle adjustments. The proposed H-MPC enables the decoupling of the low- and high-frequency stages in the IHMC and also reduces both output current ripples and computational burden while achieving a constant switching frequency simultaneously. Comprehensive simulation and experimental studies on an all silicon carbide prototype verify the effectiveness of the proposed control strategy.